Keeping the aluminum molten in just an insulated tank is pretty simple because it has a huge thermal mass. Getting it molten is also simple with just resistance coils or even tungsten halogen lights in an insulated oven (which would describe the fuel tank) because it melts at 900 to 1200F. Of course the simplest way to melt aluminum is probably with a solar reflector, after which you'd pump it into the tank.

I'd try to heat it much higher than the melting point to improve viscosity and impart a little extra energy, since extra thermal energy in the aluminum translates into better performance as a propellant. If you heat it to 900C you add about 1.2 MJ/kg to the 32.2 MJ/kg heat of combustion, probably raising the ISP from about 285 up to 290, which is servicable as a lunar propellant.

I'm not sure what experiments have been done with molten metal fuels, though. The probably questions to answer are how the injectors fair. If the engine and tank are being heated prior to launch anyway, and you only depend on one big burn to get into orbit, it wouldn't really matter if residual aluminum in the lines or injectors solidified after engine shutdown, because such an engine would only be used to launch other materials to a fuel depot or assembly station.

Extracting aluminum on the moon is relatively straightforward, since the most common mineral on the moon is anorthite (NaAlSi3O8), which we're looking at switching to because bauxite is getting harder to find. The cost is of processing anorthite is about twice that of bauxite. You're just going to need a lot of electrical power.